A temperature-dependent thermodynamic model was developed for representing the solid–aqueous equilibria in the quaternary NaCl + KCl + RbCl + H₂O system based on the previous ones for binary and ternary systems. The solid–liquid equilibria in the quaternary system were first predicted by the developed model and then verified by conducting the experiments at T = 298.15 K by an isothermal equilibrium method with equilibration times of 5 and 160 days, respectively. The predicted univariant curve saturated with NaCl(cr) and (K,Rb)Cl(ss) in the system is in good agreement with our experimental data. Moreover, to verify the reliability of the model for the prediction of solid solution composition that coexisted with NaCl(cr), the XRD quantitative analysis technique based on the inverse Vegard approach is used. The experimentally determined solid solution compositions well support the results predicted by the model, indicating that the model can simultaneously predict the compositions of aqueous solution and solid solution that coexisted with a pure salt, i.e., NaCl(cr), in a system under an equilibrium state. Finally, phase diagrams of the quaternary NaCl + KCl + RbCl + H₂O system at a temperature range of 273.15–373.15 K were predicted. These diagrams are useful for the future industrial applications.

中文翻译：

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NaCl + KCl + RbCl + H ₂ O季铵盐体系中的固-水相平衡：298.15 K时的热力学预测和实验验证

基于先前的二元和三元系统，开发了一个温度相关的热力学模型来表示四元NaCl + KCl + RbCl + H ₂ O系统中的固-水平衡。首先通过开发的模型预测四元系统中的固液平衡，然后通过在T处进行实验来验证通过等温平衡法得到的平衡时间分别为298.15 K和5天和160天。在系统中用NaCl（cr）和（K，Rb）Cl（ss）饱和的预测单变量曲线与我们的实验数据非常吻合。此外，为了验证与NaCl（cr）共存的固溶体组成预测模型的可靠性，使用了基于逆Vegard方法的XRD定量分析技术。实验确定的固溶体成分很好地支持了模型预测的结果，表明该模型可以在平衡状态下同时预测与纯盐即NaCl（cr）共存的水溶液和固溶体的成分州。最后是四元NaCl + KCl + RbCl + H _2的相图预测温度范围为273.15–373.15 K的O系统。这些图对于将来的工业应用很有用。